A Maximum Likelihood Method for Quasispecies Reconstruction Nicholas Mancuso, Georgia State University Bassam Tork, Georgia State University Pavel Skums, Centers for Disease Control Lilia Ganova-Raeva, Centers for Disease Control Ion Mandoiu, University of Connecticut Alex Zelikovsky, Georgia State University CANGS 2012

Outline Background Quasispecies spectrum reconstruction from amplicon NGS reads Ongoing and future work

Cost of DNA Sequencing

Cost/Performance Comparison [Glenn 2011]

RNA Viruses o HIV, HCV, SARS, Influenza o Higher (than DNA) mutation rates o ➔ quasispecies  set of closely related variants rather than a single species Knowing quasispecies can help o Interferon HCV therapy effectiveness (Skums et al 2011) NGS allows to find individual quasispecies sequences o 454 Life Sciences : Mb with reads bp long Sequencing is challenging o multiple quasispecies o qsps sequences are very similar  different qsps may be indistinguishable for > 1kb (longer than reads) Viral Quasispecies and NGS

Shotgun reads starting positions distributed ~uniformly Amplicon reads reads have predefined start/end positions covering fixed overlapping windows Shotgun vs. Amplicon Reads

Quasispecies Spectrum Reconstruction (QSR) Problem Given Shotgun/amplicon pyrosequencing reads from a quasispecies population of unknown size and distribution Reconstruct the quasispecies spectrum Sequences Frequencies

Prior Work Eriksson et al 2008 maximum parsimony using Dilworth’s theorem, clustering, EM Westbrooks et al min-cost network flow Zagordi et al (ShoRAH) probabilistic clustering based on a Dirichlet process mixture Prosperi et al 2011 (amplicon based) based on measure of population diversity Huang et al 2011 (QColors) Parsimonious reconstruction of quasispecies subsequences using constraint programming within regions with sufficient variability

Outline Background Quasispecies spectrum reconstruction from amplicon NGS reads Ongoing and future work

Amplicon Sequencing Challenges Distinct quasispecies may be indistinguishable in an amplicon interval Multiple reads from consecutive amplicons may match over their overlap

Prosperi et al First published approach for amplicons Based on the idea of guide distribution choose most variable amplicon extend to right/left with matching reads, breaking ties by rank

Read Graph for Amplicons K amplicons → K-staged read graph vertices → distinct reads edges → reads with consistent overlap vertices, edges have a count function

Read Graph May transform bi-cliques into 'fork' subgraphs common overlap is represented by fork vertex

Observed vs Ideal Read Frequencies Ideal frequency consistent frequency across forks Observed frequency (count) inconsistent frequency across forks

Fork Balancing Problem Given Set of reads and respective frequencies Find Minimal frequency offsets balancing all forks Simplest approach is to scale frequencies from left to right

Least Squares Balancing Quadratic Program for read offsets q – fork, o i – observed frequency, x i – frequency offset

Fork Resolution: Parsimony 8 (a) (b)

Fork Resolution: Max Likelihood Observation o Potential quasispecies has extra bases in overlap o Must be at least two instances of this quasispecies to produce both of these reads Assumption o Solution is a forest

Fork Resolution: Max Likelihood Given a forest, ML = # of ways to produce observed reads / 2^(#qsp): Can be computed efficiently for trees: multiply by binomial coefficient of a leaf and its parent edge, prune the edge, and iterate Solution (b) has a larger likelihood than (a) although both have 3 qsp’s (a) (4 choose 2) * (8 choose 4) * (8 choose 4)/2^20 = 29400/2^20 ~ 2.8% (b) (12 choose 6) * (4 choose 2)*(4 choose 2)/2^20 = 33264/2^20 ~ 3.3% 8 (a)(b)

Fork Resolution: Min Entropy Solution (b) also has a lower entropy than (a) (a) -[ (8/20)log(8/20) + (8/20)log(8/20) + (4/20)log(4/20) ] ~ (b) -[ (12/20)log(4/20) + (4/20)log(4/20) + (4/20)log(4/20) ] ~ (a)(b)

Fork Resolution: Min Entropy Local Resolution Greedily match maximum count reads in overlap Repeat for all forks until graph is fully resolved Global Resolution Maximum bandwidth paths Find s-t path, reduce counts by minimum edge, repeat until exhausted

Local Optimization: Greedy Method

Greedy Method

Global Optimization: Maximum Bandwidth

Maximum Bandwidth Method

Experimental Setup Error free reads simulated from 1739bp long fragments of HCV quasispecies - Frequency distributions: uniform, geometric, … 5k-100k reads - Amplicon width = 300bp - Shift (= width – overlap, i.e., how much to slide the next amplicon) between 50 and 250 Quality measures - Sensitivity - PPV - Jensen-Shannon divergence

Sensitivity for 100k Reads (Uniform Qsps)

PPV for 100k Reads (Uniform Qsps)

JS Divergence for 100k Reads (Uniform Qsps)

Amplicon vs. Shotgun Reads (avg. sensitivity/PPV over 10 runs)

Real HBV Data Real HBV data from two patients Sequenced using GS FLX LR25 Twenty-five amplicons were generated Error correction with KEC (Skums 2011) Aligned with MosiakAligner tool

Real HBV Data

Outline Background Quasispecies spectrum reconstruction from amplicon NGS reads Ongoing and future work

Ongoing and Future Work Correction for coverage bias Comparison of shotgun and amplicon based reconstruction methods on real data Quasispecies reconstruction from Ion Torrent reads Combining long and short read technologies Optimization of vaccination strategies

Acknowledgements University of Connecticut Rachel O’Neill, PhD. Mazhar Kahn, Ph.D. Hongjun Wang, Ph.D. Craig Obergfell Andrew Bligh Georgia State University Alex Zelikovsky, Ph.D. Bassam Tork Nicholas Mancuso Serghei Mangul University of Maryland Irina Astrovskaya, Ph.D. Centers for Disease Control and Prevention Pavel Skums, Ph.D.